1887

Abstract

Summary

Mimetic operators are a kind of discrete operators which, on staggered grids, can accomplish “mimetic” properties analogous to their continuous counterparts. Furthermore, they can attain identical convergence order everywhere in the domain, including at or near the domain’s boundaries in non-periodic problems. This property makes mimetic finite difference (MFD) operators attractive whenever high-contrast interfaces or physical boundary conditions are present in our models. In the seismic case, the strongest boundary condition is the interface between Earth and air, the so-called free surface. This surface is typically represented as a traction-free boundary condition and, although it is of critical importance for achieving accurate results, due to its vicinity to the sources and receivers, it is still a problem for current FD implementations. Despite efforts in the past, few FD schemes have attained convergence of order beyond two in results involving the free surface. Here we summarize the properties of mimetic operators applied to the elastic wave equation, as well as the changes required in order to incorporate into current explicit staggered grid codes the mimetic approach of the free-surface condition

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/content/papers/10.3997/2214-4609.201601663
2016-05-31
2020-03-31
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References

  1. Castillo, J., Hyman, J., Shashkov, M. and Steinberg, S.
    [2001] Fourth- and sixth-order conservative finite difference approximations of the divergence and gradient. Appl. Numer. Math., 37(1–2), 171–187.
    [Google Scholar]
  2. Castillo, J.E. and Miranda, G.F.
    [2013] Mimetic Discretization Methods.CRC Press, Boca Raton, Florida.
    [Google Scholar]
  3. Fornberg, B.
    [1988] Generation of Finite Difference Formulas on Arbitrary Spaced Grids. Mathematics of Computation, 51(184), 699–706.
    [Google Scholar]
  4. Kristek, J., Moczo, P. and Archuleta, R.J.
    [2002] Efficient Methods to Simulate Planar Free Surface in the 3D 4th-Order Staggered-Grid Finite-Difference Schemes. Studia Geophysica et Geodaetica, 46, 355–381. 10.1023/A:1019866422821.
    https://doi.org/10.1023/A:1019866422821 [Google Scholar]
  5. Lebedev, V.
    [1964] Difference analogies of orthogonal decompositions of basic differential operators and some boundary value problems. I. Sov. Comput. Math. Math. Phys., 4, 449–465.
    [Google Scholar]
  6. de la Puente, J., Ferrer, M., Hanzich, M., Castillo, J.E. and Cela, J.M.
    [2014] Mimetic seismic wave modeling including topography on deformed staggered grids. Geophysics, 79(3), T125–T141.
    [Google Scholar]
  7. Robertsson, J.O.A.
    [1996] A numerical free-surface condition for elastic/ viscoelastic finite-difference modeling in the presence of topography. Geophysics, 61(6), 1921–1934.
    [Google Scholar]
  8. Rojas, O., Day, S., Castillo, J. and Dalguer, L.A.
    [2008] Modelling of rupture propagation using high-order mimetic finite differences. Geophys. J. Int., 172(2), 631–650.
    [Google Scholar]
  9. Rojas, O., Dunham, E.M., Day, S.M., Dalguer, L.A. and Castillo, J.E.
    [2009] Finite difference modelling of rupture propagation with strong velocity -weakening friction. Geophysical Journal International, 179(3), 1831–1858.
    [Google Scholar]
  10. Virieux, J.
    [1986] P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method. Geophysics, 51, 889–901.
    [Google Scholar]
  11. Zeng, C., Xia, J., Miller, R.D. and Tsoflias, G.P.
    [2012] An improved vacuum formulation for 2D finite-difference modeling of Rayleigh waves including surface topography and internal discontinuities. Geophysics, 77(1), T1–T9.
    [Google Scholar]
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